Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/on-bi-lyapunov-stable-homoclinic-classes-hQ0O01qlGX
References (32)
-
Dawei Yang, Shaobo Gan (2008)
Expansive homoclinic classesNonlinearity, 22
-
E. Pujals, Mart'in Sambarino (2000)
Homoclinic tangencies and hyperbolicity for surface diffeomorphismsAnnals of Mathematics, 151
-
C. Bonatti, S. Crovisier, L. D'iaz, N. Gourmelon (2010)
Internal perturbations of homoclinic classes: non-domination, cycles, and self-replicationErgodic Theory and Dynamical Systems, 33
-
R. Potrie, Mart'in Sambarino (2008)
Codimension one generic homoclinic classes with interiorBulletin of the Brazilian Mathematical Society, New Series, 41
-
J. Franks (1971)
Necessary conditions for stability of diffeomorphismsTransactions of the American Mathematical Society, 158
-
J. Palis (2005)
A global perspective for non-conservative dynamicsAnnales De L Institut Henri Poincare-analyse Non Lineaire, 22
-
R. Bott (1996)
ON INVARIANTS OF MANIFOLDS -
R. Mãné (1982)
An Ergodic Closing LemmaAnnals of Mathematics, 116
-
N. Gourmelon (2009)
A Franks’ lemma that preserves invariant manifoldsErgodic Theory and Dynamical Systems, 36
-
J Palis (2005)
A global perspective for non-conservative dynamicsAnn. Inst. H. Poincaré Anal. Non Linéaire, 22
-
K. Sakai, Naoya Sumi, Kenichiro Yamamoto (2010)
DIFFEOMORPHISMS SATISFYING THE SPECIFICATION PROPERTY, 138
-
F. Abdenur, C. Bonatti, S. Crovisier, Lorenzo Casado, L. Wen (2006)
Periodic points and homoclinic classesErgodic Theory and Dynamical Systems, 27
-
J Palis, W Melo (1982)
Anintroduction -
X. Wen, Shaobo Gan, L. Wen (2009)
C 1 -STABLY SHADOWABLE CHAIN COMPONENTS ARE HYPERBOLICJournal of Differential Equations, 246
-
F Abdenur, L Diaz (2007)
Pseudo-orbit shadowing in the C 1 topologyDiscrete Contin. Dyn. Syst., 17
-
C. Carballo, C. Morales, M. Pacifico (2001)
Homoclinic classes for generic C^1 vector fieldsErgodic Theory and Dynamical Systems, 23
-
K. Sigmund (1970)
Generic properties of invariant measures for AxiomA-diffeomorphismsInventiones mathematicae, 11
-
M Sambarino, J Vieitez (2006)
On persistently expansive homoclinic classesDiscrete Contin. Dyn. Syst., 14
-
CM Carballo, CA Morales, MJ Pacifico (2003)
Homoclinic classes for generic C 1 vector fieldsErgodic Theory Dynam. Systems, 23
-
X Wen, S Gan, L Wen (2009)
C 1-stably shadowable chain components are hyperbolicJ. Differential Equations, 246
-
S. Smale (1967)
Differentiable dynamical systemsBulletin of the American Mathematical Society, 73
-
F. Abdenur, L. Díaz (2006)
Pseudo-orbit shadowing in the $C^1$ topologyDiscrete and Continuous Dynamical Systems, 17
-
J. Robbin, J. Palis, W. Melo (1984)
Geometric theory of dynamical systems : an introductionAmerican Mathematical Monthly, 91
-
J. Zukas (1998)
Introduction to the Modern Theory of Dynamical SystemsShock and Vibration, 5
-
Christian Bonatti, Sylvain Crovisier (2003)
Récurrence et généricitéInventiones mathematicae, 158
-
S. Pilyugin (1999)
Shadowing in dynamical systems -
N. Haydn, D. Ruelle (1992)
Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specificationCommunications in Mathematical Physics, 148
-
F. Abdenur (2003)
Attractors of generic diffeomorphisms are persistentNonlinearity, 16
-
J. Palis, W. Melo (1982)
Geometric theory of dynamical systems -
R. Potrie (2009)
Generic bi-Lyapunov stable homoclinic classesNonlinearity, 23
-
F. Abdenur (2003)
Generic robustness of spectral decompositionsAnnales Scientifiques De L Ecole Normale Superieure, 36
-
F. Abdenur, C. Bonatti, L. Díaz (2004)
Non-wandering sets with non-empty interiorsNonlinearity, 17
- Publisher
- Springer Journals
- Copyright
- Copyright © 2013 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-013-0005-y
- Publisher site
- See Article on Publisher Site
Abstract
For a C 1 generic diffeomorphism if a bi-Lyapunov stable homoclinic class is homogeneous then it does not have weak eigenvalues. Using this, we show that such homoclinic classes are hyperbolic if it has one of the following properties: shadowing, specification or limit shadowing.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Jun 25, 2013